Variable Selection In Linear Model And The Empirical Research On Stock Market

The linear regression analysis is the most widely used method of the multivariate statistical analysis methods, The purpose is to research the relationship between a plurality of interdependent variables. And there is an important issue in the process of establishing the regression model: How to select the most influential variables on the response variable from numerous explanatory variables, namely variable selection problem. Variable selection in modern statistics is becoming more and more important.Among them, the method named "Lasso" proposed by Tibshirani in 1996 is sought by scholars. With the development of computer technology, at this stage, "Lasso" method has been used in all kinds of models to solve variables selection problem.This paper mainly applies the "Lasso" method to the regression model, and carries the empirical research in the stock market. First, startting from the multiple regression analysis,this paper introduces the development of the biased estimates in linear regression model and some variable selection methods in the linear model which is used commonly. Secondly, the paper explaines "Lasso" methods in detail, include the definition of "Lasso", Lars algorithms and other "Lasso" related methods and so on. To make the empirical research, the paper selectes five minutes timesharing data of the SSE 50 Index to be the dependent variable, and make the 50 shares’ 5 minutes closing price in the same time zone those composite the SSE 50 Index to be independent variable.Based on the regression model of SSE 50 Index and the 50 stocks, the paper uses the "Lasso" methods, Lars algorithms,and R software to solve the model. We select out19 constituent stocks which have larger influence on the SSE 50 Index successfully. By way of further, in the fitting analysis, we find that the model the effect is very good. At last, the paper adds the weights in the model to access more information about the argument, and finds that after the introduction of the weight,the effect is better, the trend of fitting value and the true value are closer. So this paper can be a part of reference for the Investors to predict the stock market dynamic.